JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of permutation, Number of permutations with or without repetition, Conditional permutations

  • question_answer
    The number of 5 digit telephone numbers having at least one of their digits repeated is [Pb. CET 2000]

    A) 90,000

    B) 100,000

    C) 30,240

    D) 69,760

    Correct Answer: D

    Solution :

    Using the digits 0, 1, 2, ......, 9 the number of five digit telephone numbers which can be formed is \[{{10}^{5}}\] (since repetition is allowed) The number of five digit telephone, numbers which have none of the digits repeated = \[^{10}{{P}_{5}}=30240\]. \[\therefore \]The required number of telephone numbers = \[5\times 4=20\].

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